Question

An automobile manufacturer would like to know what proportion of its customers are dissatisfied with the service received from their local dealer. The customer relations department will survey a random sample of customers and compute a 95% confidence interval for the proportion that are dissatisfied. From past studies, it believes that this proportion will be about 0.24. Find the sample size needed if the margin of error of the confidence interval is to be no more than 0.03. (Round your answer up to the next whole number.)

Answer 1

Solution:

Given that,

= 0.24

1 - = 1 - 0.5 = 0.76

margin of error = E = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z _{/ 2}) / E)² * * (1 - )

= (1.960 / 0.03)² * 0.24 * 0.76

= 774.592

= 775

n = sample size = 775